Revista Matemática Iberoamericana
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Published online: 2019-05-09
Polynomial bounds for automorphisms groups of foliations
Maurício Corrêa[1] and Alan Muniz[2] (1) Universidade Federal de Minas Gerais, Belo Horizonte, Brazil(2) Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
Let $(X, \mathcal{F})$ be a foliated surface and $G$ a finite group of automorphisms of $X$ that preserves $\mathcal{F}$. We investigate invariant loci for $G$ and obtain upper bounds for its order that depends polynomially on the Chern numbers of $X$ and $\mathcal{F}$. As a consequence, we estimate the order of the automorphism group of some foliations under mild restrictions. We obtain an optimal bound for foliations on the projective plane which is attained by the automorphism groups of the Jouanolou's foliations.
Keywords: Automorphism, holomorphic foliations
Corrêa Maurício, Muniz Alan: Polynomial bounds for automorphisms groups of foliations. Rev. Mat. Iberoam. 35 (2019), 1153-1194. doi: 10.4171/rmi/1081